| Displaying 1-9 of 9 results found.
page
1
a(n) is the conjectured highest power of n which has no three identical digits in succession.
+10
9
1583, 1175, 774, 1359, 776, 607, 516, 579, 2, 472, 390, 460, 812, 426, 387, 800, 502, 476, 2, 400, 472, 387, 298, 382, 466, 386, 249, 374, 2, 238, 237, 289, 243, 338, 388, 254, 189, 263, 2, 481, 442, 389, 398, 232, 412, 296, 284, 261, 2, 216, 329, 367, 341, 271, 186, 349, 340, 236
a(n) is the conjectured highest power of n which has no four identical digits in succession.
+10
8
35864, 19590, 17932, 14103, 9702, 10061, 8892, 9795, 3, 6889, 8069, 8742, 6448, 6553, 8966, 4594, 6800, 6670, 3, 4869, 5061, 5635, 6001, 3784, 6450, 6530, 4631, 4930, 3, 4777, 4947, 6889, 4902, 5220, 4851, 4276, 3281, 4541, 3, 3679, 5302, 5279, 5271, 3317, 4296, 4331, 4930, 4921
Greatest integer k such that n^i has no identical consecutive digits for i = 0..k.
+10
4
15, 10, 7, 10, 4, 5, 5, 5, 1, 0, 1, 8, 2, 1, 3, 6, 4, 4, 1, 1, 0, 5, 3, 5, 4, 3, 7, 4, 1, 5, 4, 0, 1, 1, 2, 6, 1, 3, 1, 4, 2, 3, 0, 2, 1, 1, 2, 2, 1, 6, 3, 2, 5, 0, 3, 3, 1, 3, 1, 2, 1, 2, 2, 1, 0, 1, 2, 3, 1, 2, 6, 5, 2, 5, 1, 0, 2, 3, 1, 2, 2, 1, 4, 1, 3, 5, 0
EXAMPLE
a(2) = 15 because the powers of 2 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536 and only the 16th power has consecutive identical digits.
MATHEMATICA
Table[k = 1; While[! MemberQ[Differences[IntegerDigits[n^k]], 0], k++]; k = k - 1, {n, 2, 100}]
CROSSREFS
Cf. A216063 (highest power of n having different consecutive digits), A217157.
a(n) = conjectured number of integers k such that n^k has no two consecutive identical digits.
+10
1
40, 24, 22, 23, 10, 12, 14, 13, 1, 8, 7, 10, 10, 8, 12, 8, 6, 6, 1, 6, 6, 9, 6, 12, 8, 9, 8, 10, 1, 8, 8, 6, 5, 6, 5, 8, 8, 5, 1, 10, 5, 4, 7, 8, 6, 4, 6, 5, 1, 6, 6, 8, 7, 6, 6, 6, 4, 5, 1, 7, 5, 5, 8, 5, 4, 4, 3, 6, 1, 4, 7, 5, 5, 8, 3, 4, 5, 7, 1, 4, 6, 7, 6
MATHEMATICA
Table[cnt = 0; Do[If[! MemberQ[Differences[IntegerDigits[n^k]], 0], cnt++], {k, 1000}]; cnt, {n, 2, 100}] (* T. D. Noe, Sep 20 2012 *)
a(n) = conjectured number of integers k such that n^k has no three consecutive identical digits.
+10
1
335, 246, 164, 150, 141, 137, 109, 120, 2, 93, 79, 105, 105, 98, 85, 82, 76, 89, 2, 79, 79, 80, 72, 74, 71, 85, 79, 83, 2, 78, 62, 70, 76, 78, 75, 75, 67, 68, 2, 70, 70, 70, 67, 61, 65, 60, 60, 71, 2, 77, 74, 67, 63, 69, 69, 58, 62, 57, 2, 68, 60, 67, 47, 62
Conjectured number of digits in highest power of n with no two consecutive identical digits.
+10
1
38, 64, 38, 23, 21, 23, 38, 32, 2, 17, 17, 13, 88, 18, 32, 24, 23, 11, 2, 60, 52, 26, 17, 23, 43, 32, 16, 31, 2, 24, 25, 17, 19, 17, 21, 16, 37, 16, 2, 36, 31, 10, 30, 42, 39, 19, 17, 11, 2, 11, 14, 35, 25, 30, 20, 23, 25, 24, 2, 27, 26, 31, 38, 30, 30, 17, 8
COMMENTS
Number of digits in n^k is equal to A055642(n^k) = floor(1+k*log_10(n)). - V. Raman, Sep 27 2012
MATHEMATICA
Table[mx = 0; Do[If[! MemberQ[Differences[d = IntegerDigits[n^k]], 0], mx = Length[d]], {k, 1000}]; mx, {n, 2, 50}] (* T. D. Noe, Oct 01 2012 *)
Conjectured number of digits in highest power of n with no three consecutive identical digits.
+10
1
477, 561, 466, 950, 604, 513, 466, 553, 3, 492, 421, 513, 931, 502, 466, 985, 631, 609, 3, 529, 634, 527, 412, 535, 660, 553, 361, 547, 3, 355, 357, 439, 373, 522, 604, 399, 299, 419, 4, 776, 718, 636, 655, 384, 686, 495, 478, 442, 4, 369, 565, 633, 591, 472
COMMENTS
The number of decimal digits in n^k is equal to A055642(n^k) = floor(1+k*log_10(n)). - V. Raman, Sep 27 2012
a(n) = conjectured number of integers k such that n^k has no four consecutive identical digits.
+10
0
3674, 2385, 1836, 1608, 1438, 1333, 1239, 1201, 3, 1040, 1001, 978, 980, 948, 929, 881, 914, 852, 3, 828, 818, 834, 820, 819, 779, 786, 762, 750, 3, 708, 753, 759, 738, 676, 709, 685, 761, 703, 3, 703, 728, 707, 660, 675, 667, 633, 649, 660, 3
Conjectured number of digits in highest power of n with no four consecutive identical digits.
+10
0
10797, 9347, 10797, 9858, 7550, 8503, 8031, 9347, 4, 7175, 8708, 9739, 7391, 7707, 10797, 5653, 8536, 8530, 4, 6438, 6795, 7674, 8283, 5290, 9127, 9347, 6702, 7210, 5, 7125, 7446, 10462, 7508, 8061, 7550, 6706, 5184, 7226, 5, 5934, 8607, 8624, 8663, 5484
COMMENTS
The number of decimal digits in n^k is equal to A055642(n^k) = floor(1+k*log_10(n)). - V. Raman, Sep 27 2012
Search completed in 0.005 seconds
|